# math/algebra

Use the exponential decay equation, to find the half-life of a material that decays from 40mg to 30mg in 10 hours.

1. 👍 0
2. 👎 0
3. 👁 115
1. 30 = 40e^10k
.75 = e^10k
10k = ln.75
k = ln.75/10 = -.028768

then
1/2 = e^-.028768t
- .028768t = ln .5
t = ln .5/-.028768 = 24.09

the half-life is appr. 24.1 hours

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Math

A radioactive substance decays according to the formula Q(t) = Q0e−kt where Q(t) denotes the amount of the substance present at time t (measured in years), Q0 denotes the amount of the substance present initially, and k (a

2. ### Exponential Growth and Decay

Can somebody please check my answers? 1. Identify the initial amount a and the growth factor b in the exponential function. g(x)=14*2^x a)a=14, b=x b)a=14, b=2

3. ### Calculus-Modeling Equations

An unknown radioactive element decays into non-radioactive substances. In 420 days the radioactivity of a sample decreases by 39 percent. 1.What is the half-life of the element? 2.How long will it take for a sample of 100 mg to

4. ### Algebra 2 help...

A half life of a certain radioactive is 36 days. An initial amount of the material has a mass of 487 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 5

1. ### math

6. The half-life of a certain radioactive material is 32 days. An initial amount of the material has a mass of 361 kg. Write an exponential function that models the decay of this material. Find how much radioactive material

2. ### Chemistry

What is the half-life of sodium-24? Explain how you determined your answer. Sodium-24 decays by beta emission. Write a nuclear equation that shows the decay of sodium-24 and its products.

3. ### calculus

Carbon-14 is a radioactive substance produced in the Earth's atmosphere and then absorbed by plants and animals on the surface of the earth. It has a half-life (the time it takes for half the amount of a sample to decay) of

4. ### math

You have just isolated a new radioactive element. If you can determine its half-life, you will win the Nobel Prize in physics. You purify a sample of 2 grams. One of your colleagues steals half of it, and eight days later you find

1. ### Calculus

The rate of decay is proportional to the mass for radioactive material. For a certain radioactive isotope, this rate of decay is given by the differential equation dm/dt = -.022m, where m is the mass of the isotope in mg and t is

2. ### math

8. The half-life of a certain radioactive material is 71 hours. An initial amount of the material has a mass of 722 kg. Write an exponential function that models the decay of this material. Find how much radioactive material

3. ### Alg2

Radioactive iodine is used to determine the health of the thyroid gland. It decays according to the equation y=ae -0.0856t where t is in days. Find the half-life of this substance. Round to the tenths place.

4. ### Alg2

Radioactive iodine is used to determine the health of the thyroid gland. It decays according to the equation y=ae -0.0856t where t is in days. Find the half-life of this substance. Round to the tenths place.